So many different hunts in the responses above! Love it!
You asked about favorite big game hunts... I have to admit that my favorite hunt is for upland birds, pheasant in particular, with my dog, my family and friends.
But... for big game... Wow... About the time I decide I like something best... I try something else.
Mostly I hunt mule deer. There's a good population of them in my local area here in central Washington, and I can hunt them either up in the Cascade Mountains, or out on the sagebrush covered plateau to the east. Either way has an attraction for me, and I've done pretty well both places. Usually I'm hunting with friends and family, sometimes alone.
I also go to Wyoming for mule deer every couple of years. I hunt a large private ranch there, and it is indeed something special to share a 40,000 acre ranch with only one or two other hunters! Think about something like that, it really is quality hunting. The animals are largely undisturbed by other hunters, and are pretty much just going about their business every day.
Antelope hunting in Wyoming is an absolute blast! I've only hunted them in October, four times, and each time managed to take a buck. I've stalked and failed to take a couple of real whoppers! Always seem to "settle" for an average buck. That's fine, the backstrap steaks are delicious!
I haven't done enough elk hunting to call it my favorite. Have taken one good 6x6 bull on a wilderness hunt. We packed on horses, set up a traditional western tent camp and hunted from there. It was an outstanding experience, highly recommended!
Later, took a nice fat cow elk here in Washington, only a few miles from home, on a DIY late season hunt. Also fun, fairly challenging, and again, delicious meat!
Bear hunting... This really got me worked up... Good population of black bear, in several different colors, here in Washington. All spot & stalk here, no dogs, no bait. It can be challenging. Managed to call one in with a predator call! That was INTENSE. Photo is of a bear my son took a few years ago:
I think each hunt has a distinct flavor and appeal to it. When I was younger I tended to do more backpacking hunts for high country mule deer. I may do that again this year, but maybe not. There are a lot of different possibilities and I think you ought to figure out which one appeals to you the most, now. Priorities may change later.
Mostly I value the experience of the hunt. I've been able to tag a good number of big game animals over the years, but that's not the only way to measure success. I'm happy when I've had a "good" hunt. Happier when that hunt fills the freezer.
Regards, Guy